Implicative subreducts of MV-algebras: free and weakly projective objects

CASTAÑO, DIEGO NICOLÁS

ALGEBRA UNIVERSALIS

BIRKHAUSER VERLAG AG

Año: 2017 vol. 78 p. 579 - 600

0002-5240

In this article, we explore in some detail the free and weakly projective objects of the variety of Łukasiewicz implication algebras (the implicative subreducts of MV-algebras). We review the two already known descriptions of finitely generated free algebras, giving new insights into their structure and their connection, as well as providing new proofs of the characterizations. We give a representation theorem for weakly projective algebras as algebras of certain McNaughton functions restricted to rational polyhedra and prove that finitely generated weakly projective algebras coincide with finitely presented ones. We also prove that finite chains are the only totally ordered weakly projective examples in this variety.